Solve for $x$ : $2x^2 + 2x - 180 = 0$
Solution: Dividing both sides by $2$ gives: $ x^2 + {1}x {-90} = 0 $ The coefficient on the $x$ term is $1$ and the constant term is $-90$ , so we need to find two numbers that add up to $1$ and multiply to $-90$ The two numbers $-9$ and $10$ satisfy both conditions: $ {-9} + {10} = {1} $ $ {-9} \times {10} = {-90} $ $(x {-9}) (x + {10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -9) (x + 10) = 0$ $x - 9 = 0$ or $x + 10 = 0$ Thus, $x = 9$ and $x = -10$ are the solutions.